The two-grid discretization of Ciarlet-Raviart mixed method for biharmonic eigenvalue problems

摘要

In this paper, for biharmonic eigenvalue problems with clamped boundary condition in R-n which include plate vibration problem and plate buckling problem, we primarily study the two-grid discretization based on the shifted-inverse iteration of Ciarlet-Raviart mixed method. With our scheme, the solution of a biharmonic eigenvalue problem on a fine mesh pi(h) can be reduced to the solution of an eigenvalue problem on a coarser mesh pi(H) and the solution of a linear algebraic system on the fine mesh pi(h). With a new argument which is not covered by existing work, we prove that the resulting solution still maintains an asymptotically optimal accuracy when H h = O(H-2). The surprising numerical results show the efficiency of our scheme. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.